CFD|NFX湍流本构-上
It is not easy to simulate, predict and control turbulence due to its complexity. DNS (Direct Numerical Simulation) that directly simulates turbulence behavior by the Navier-Stokes equation requires great number of analysis meshes. Variety of turbulence modeling has been proposed to address this issue. Turbulence is achieved by definition on turbulent viscosity. However, since turbulent viscosity is not directly derivable from the theoretical equation, it is calculated by assumption on the equation on average change rate of turbulence variable. The process that assumes the equation on average change rate of turbulence variable and calculates turbulent viscosity from it is called turbulence modeling. The turbulence modeling is largely divided into the turbulence model such as
model and
model that use the transport equation of turbulence variable derived from the RANS (Reynolds Averaged Navier-Stokes) equation, and the LES LES(Large Eddy Simulation) model that simulates big eddies only by using the fact that turbulence does not occur throughout the entire domain of fluid flow.
Turbulence Variable and Kolmogorov Scale
When conducting flow analysis using a mesh in a specific size, dissipation rates of the eddy kinetic energy and the turbulence energy dissipated by eddy in the Kolmogorov scale that indicates the smallest eddy size able to simulate act as critical variables in describing turbulence. Turbulent kinetic energy is indicated in mass density with respect to fluid unit mass, and is defined by velocity fluctuation from average field calculated by RANS calculation as follows
By turbulent kinetic energy, turbulent energy dissipation rate is calculated as follows. The negative (-)code is to design for the dissipation rate to be positive (+) on turbulent energy dissipation.
Motion of turbulence in the small scale is determined by the turbulent energy dissipation rate ε and the fluid kinematic viscosity. It is possible to define length, time and velocity Kolmogorov scales η，
and 
by dimensional approach of variables as follows.
Meanwhile, turbulence Reynolds numbers can be defined based on turbulent energy dissipation rate and turbulent energy specific dissipation rate as follow.
Turbulence Modeling Classification
Following is the Navier-Stokes equation of general compressible flow.
For incompressible flow, the last term in the right side disappears from the mass conservation equation
=0, and the incompressible RANS equation is derived from it as follows. Turbulence modeling is applied to simulate the turbulence shear stress term which is the last term of the equation (4.2.8).
If the turbulent viscosity concept the same as viscosity is introduced to the turbulence shear stress term and 
that velocity gradient is multiplied on it is substituted, the equation is derived as follows.
Turbulent kinematic viscosity is expressed as multiplication of the velocity scale V and length scale L as follows, and each turbulence modeling differs in the way to derive V and L.
Turbulence modeling is largely divided into the RANS equation model and the LES model, and it can be classified as illustrated in Figure 4.2.1.
RANS Equation Model
0-equation model
1-equation model
2-equation model
model calculates transport equations for k and ε then it calculates L by the equation as follows.
In addition the model calculates transport equations for k and ε then it calculates L as follows
LES model
The LES model is the model to simulate large scale turbulence flows only. The small eddy is analyzed by the Navier-Stokes equation (4.2.7) and the big eddy is calculated as like the equation (4.2.9) using the turbulent viscosity concept. For modeling complex flow problems, usability of the LES model increases.However, for accurate calculation, it requires the DES level mesh finer than the RANS equation turbulence model as approaching closer to the boundary layer.
